cp's OEIS Frontend

A302602 Numbers that are powers of a prime number whose prime index is either 1 or also a prime number.

%I A302602 #8 Apr 11 2018 02:55:17
%S A302602 1,2,3,4,5,8,9,11,16,17,25,27,31,32,41,59,64,67,81,83,109,121,125,127,
%T A302602 128,157,179,191,211,241,243,256,277,283,289,331,353,367,401,431,461,
%U A302602 509,512,547,563,587,599,617,625,709,729,739,773,797,859,877,919
%N A302602 Numbers that are powers of a prime number whose prime index is either 1 or also a prime number.
%C A302602 A prime index of n is a number m such that prime(m) divides n.
%e A302602 25 is in the sequence because 25 = prime(3)^2 and 3 is a prime number.
%e A302602 Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set systems.
%e A302602 01: {}
%e A302602 02: {{}}
%e A302602 03: {{1}}
%e A302602 04: {{},{}}
%e A302602 05: {{2}}
%e A302602 08: {{},{},{}}
%e A302602 09: {{1},{1}}
%e A302602 11: {{3}}
%e A302602 16: {{},{},{},{}}
%e A302602 17: {{4}}
%e A302602 25: {{2},{2}}
%e A302602 27: {{1},{1},{1}}
%e A302602 31: {{5}}
%e A302602 32: {{},{},{},{},{}}
%e A302602 41: {{6}}
%e A302602 59: {{7}}
%e A302602 64: {{},{},{},{},{},{}}
%e A302602 67: {{8}}
%e A302602 81: {{1},{1},{1},{1}}
%e A302602 83: {{9}}
%t A302602 Select[Range[1000],#===1||MatchQ[FactorInteger[#],{{_?(#===2||PrimeQ[PrimePi[#]]&),_}}]&]
%o A302602 (PARI) isok(n) = (n==1) || ((isprimepower(n, &p)) && ((p==2) || isprime(primepi(p)))); \\ _Michel Marcus_, Apr 10 2018
%Y A302602 Cf. A000961, A001222, A003963, A005117, A007425, A007716, A056239, A275024, A281113, A295931, A301764, A302242, A302243.
%K A302602 nonn
%O A302602 1,2
%A A302602 _Gus Wiseman_, Apr 10 2018